The importance of a cladistic approach in reconstructing the phylogeny of bryophytes is discussed and illustrated by an analysis of the major groups of bryophytes with respect to the tracheophytes and the green algae. The cladistic analysis, using 51 characters taken from the literature, gives the following tentative results: (1) the embryophytes as a whole are monophyletic; (2) the bryophytes (sensu lato) are paraphyletic; (3) the mosses share a more recent common ancestor with the tracheophytes than do the liverworts or hornworts; (4) the hornworts appear to share a more recent common ancestor with the moss-tracheophyte lineage than with the liverworts; however, the existence of several homoplasies makes this placement more problematical; (5) the origin of alternation of generations in the embryophytes, based on out-group comparison with their oogamous, haplontic, algal sister groups, was by progressive elaboration of the primitively epiphytic sporophyte generation; and (6) the presence of vascular tissue (xylem and phloem) can best be interpreted as a synapomorphy of the moss-tracheophyte clade, and tracheids (xylem with ornamented walls) as a synapomorphy of the tracheophytes; therefore, the prevailing designation of “vascular plants” for the tracheophytes alone is inaccurate.